Hi gb

Firstly, low temperature heat is harder to use than high temperature heat - thermodynamics again.

Second, there's a theorem that an enclosed heat-source will cause its enclosure to rise to a temperature sufficiently high to allow all its generated heat to escape. Enclose the Sun in an insulator and the inner surface temperature will become hotter than the ordinary black-body temperature of the radiation at that radial distance until its outer-skin reaches that temperature to let the heat escape. For example ten metres of shell with a heat transfer coefficient of 4 W/m.K. If the radial distance of the enclosing Dyson shell has an unobstructed regular black-body temperature of 293 K (20 C) then it's radiating 418 W/m2 on the outer surface. But what temperature does the inner surface have to be to get through the shell?

Heat tranfer: Q-dot = k(delta-T)/x

k - heat transfer coefficient; delta-T - temperature differential; x - thickness of material...

thus delta-T is (418 W)/(4/10) = 1045 K, which means things are 'toasty' on the inner side of the shell. In this case the k value is that of ice, which isn't the best choice. A nicely conductive metal would be a better choice.

Or active heat management, of course, carrying heat to big fat radiators.